A lidar (laser radar) gun is an alternative to the standard radar gun that uses

Question

A lidar (laser radar) gun is an alternative to the standard radar gun that uses the Doppler effect to catch speeders. A lidar gun uses an infrared laser and emits a precisely timed series of pulses of infrared electromagnetic waves. The time for each pulse to travel to the speeding vehicle and return to the gun is measured. In one situation a lidar gun is a stationary police car observes a difference of 1.11 × 10-7 s in round-trip travel times for two pulses that are emitted 0.510 s apart. Assuming that the speeding vehicle is approaching the police car essentially head-on, determine the speed of the vehicle.

Explanation / Answer

The first pulse travels a distance 2d more than the second pulse, in a time that is 1.11 × 10-7 s more than the first pulse.

so 2d = ct1

d = ct1 / 2 = (3*108)(1.11*10-7) / 2 = 16.65 m

speed of the car is

v = d/t2 = 16.65 / 0.510 = 32.64 m/s

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